The 4% retirement rule is broken

If there is one thing that can capture the imagination of the public when it comes to money, it's a simple rule of thumb.

That has been part of the appeal of the so-called "4 percent rule"—an investment-income strategy that says as long as you withdraw no more than 4 percent of your initial portfolio, adjusted for inflation, on an annual basis during your retirement years, you shouldn't run out of money.

However, new research shows that this rule doesn't work for retirees in today's low-rate environment. Here's why.

Quest for stability

When the formula was introduced in the early 1990s, it was designed to accomplish these goals of retirees:

But while, in the public's imagination, the 4 percent figure remained fixed, the rates it relied on were anything but. Twenty years ago, when the rule appeared, the yield on a three-month Treasury bill was 6 percent.

So while the 4 percent model called for a 50/50 stock/bond allocation, even those with a more conservative asset allocation could still draw down 4 percent annually adjusted for inflation and reasonably expect to preserve their capital. Even in 2002, the five-year U.S. Treasury yield was still 4.5 percent.

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That's no longer the case.

Today a three-month Treasury is close to 0 percent, and the five-year is less than 2 percent. In fact, at least one paper has speculated that the apparent success of the 4 percent rule during the last 20 years may have been dependent on specific market conditions—which have become less and less favorable—and called its success an "anomaly."

It makes sense that the rule's rise to popularity was a happy accident when you consider that the first decade after the model was created was an exceptional time of low inflation and high corporate earnings in the U.S.

Fly in the ointment

But even without changes in the economic climate, the last couple of decades have highlighted several other, fundamental flaws in this approach:

The 4 percent rule is based on the portfolio's initial balance; subsequent market performance isn't dynamically factored into the withdrawal rate—even though it can dramatically affect the portfolio's balance. Flat-rate withdrawals that ignore dramatic market changes can lead to premature portfolio depletion.

Likewise, a flat withdrawal rate doesn't take into account personal changes in health or lifestyle that naturally occur with age. Many retirees need more flexibility in their cash flow to handle the inevitable ups and downs of life.

In particular, an unfavorable market climate in the early years of retirement, coupled with a rigid withdrawal formula, increases the risk of asset depletion, because capital preservation during those early years is critical to the portfolio's ongoing growth.

Conversely, if returns are higher than expected in the early phase of retirement but your withdrawals are static, you run the risk of leaving money on the table at the end of your life that could have been used for greater enjoyment in previous years.

"The smartest algorithms are optimized to balance the dual objectives of maximizing lifetime withdrawals and keeping the withdrawal amount within a consistent range year after year."

So what's the modern-day retiree to do?

Fortunately, technology has come a long way since the 1990s. There is an emerging class of services from tech-savvy investment managers that provide dynamic withdrawal rates using algorithms that look at market performance, balance and term of portfolio, all of which work together to ensure you won't run out of money.

Dealing with a variable retirement income from year to year is a relatively new idea. However, the smartest algorithms are optimized to balance the dual objectives of maximizing lifetime withdrawals and keeping the withdrawal amount within a consistent range year after year.

Best of all, by working with some natural ups and downs in your income each year, you may be actually improving your overall outcome.

—By Jon Stein, special to CNBC.com. Stein is founder and CEO of Betterment, which ranked 45th on the 2014 CNBC Disruptor 50 list. The firm offers Web-based money-management services.

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